The Non-Uniform Perebor Conjecture for Time-Bounded Kolmogorov Complexity is False

ePrint Report: The Non-Uniform Perebor Conjecture for Time-Bounded Kolmogorov Complexity is False

Noam Mazor, Rafael Pass

The Perebor (Russian for “brute-force search”) conjectures, which date back to the 1950s and 1960s are some of the oldest conjectures in complexity theory. The conjectures are a stronger form of the NP ̸ = P conjecture (which they predate) and state that for “meta-complexity” problems, such as the Time-bounded Kolmogorov complexity Problem, and the Minimum Circuit Size Problem, there are no better algorithms …

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